Retrospective robustness of the continual reassessment method.

We study model sensitivity of the continual reassessment method (CRM). The context is that of dose-finding designs where certain design parameters are fixed by the investigator. Although our focus is on the CRM (O'Quigley et al., 1990), the essential ideas can be applied to any sequential dose-finding method. It is expected that different choices of a model family and particular parameterizations will have an impact on performance. Assuming that the constraints outlined in Shen and O'Quigley (1996) are respected, large sample performance is unaffected. However small sample performance will be affected by these choices, which are to some degree arbitrary. This work focuses on the retrospective robustness of the CRM in practice. The question is not of a general theoretical nature where, in the background, we would want to consider large numbers of true potential situations. Instead, the question is raised in the specific context of any actual completed study and is the following: Would we have come to the same conclusion concerning the MTD had we worked with a design specified differently? The sequential nature of the CRM means that this question cannot be answered in any definitive way. We can, though, by appealing to the retrospective CRM (O'Quigley, 2005), provide consistent estimates of the relationships between the MTD and the chosen model. If these estimates suggest that changes in different family model parameters will be accompanied by changes in final recommendation, then we would not be confident in the reliability of the estimated MTD and more work would be needed. Also, of course, at the planning stage, prospective robustness could be studied by simulating trials using particular models and parameterizations.